A.A.
Jen is exactly right. That is exactly what causes your tube to rupture. If you are 4-5 weeks along, then it is probably the right treatment. I know exactly how you feel as I have been in your shoes. I was about 14 weeks along when my doctor opted for the shot, which was way too far along to go that route. My tube did rupture and I would have died had I not been in the right place at the right time.
As for the side effects, I didn't really have any from the shot. I was tired and still feeling quite a bit of pain, but that was probably more from the ectopic pregnancy itself and the blood loss. I ruptured about 4 days after the shot.
I know you are probably very scared, upset, and worried, but please do not hesitate to convo me if you have any questions. I am so incredibly sorry you are having to go through this. It's truly a terrible thing that most folks don't understand.